A feedback structure stabilizing an n-fold integrator with even n is proposed. It is
well known that for many differential systems, in particular, for models of mechanical systems,
stabilization problems can be transformed into a special form containing a chain of integrators
as a subsystem. The control constructed for an arbitrary even order of the integrator is a linear
combination of coordinates of the delay state with odd indices and depends on three numerical
parameters. These parameters satisfy constraints of a simple form and can vary widely depending
on the control performance requirements. Examples of more general system structures are
given for which the control constructed ensures the asymptotic stability of the equilibrium. The
stability properties of cascade delay systems are used to prove the stabilizing properties of the
control.